Acronym paccarnit Name partially contracted cellirhombated penteractitriacontiditeron Circumradius ... Lace cityin approx. ASCII-art ``` x3o4x o3x4x x3o4x -- pacsrit x3o4x u3o4x x3x4x u3o4x x3o4x -- pacprit o3x4x x3x4x x3o4w x3x4x o3x4x -- pacproh o3x4x x3x4x x3o4w x3x4x o3x4x -- pacproh x3o4x u3o4x x3x4x u3o4x x3o4x -- pacprit x3o4x o3x4x x3o4x -- pacsrit | | | | +-- o3x3o4x (srit) | | | +--------- x3x3o4x (prit) | | +---------------- x3o3x4x (proh) | +----------------------- x3x3o4x (prit) +------------------------------ o3x3o4x (srit) ``` Coordinates (sqrt(2); (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)                 & all permutations within all but first coord, all changes of sign (1/sqrt(2); (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)           & all permutations within but first coord, all changes of sign (0; (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)       & all permutations within but first coord, all changes of sign Confer uniform relative: sart   carnit   prohp   general polytopal classes: partial Stott expansions

This CRF polyteron can be obtained from carnit by partial Stott contraction only within a single axial direction. Thence it is just the withdrawel of the medial prohp segment therefrom.

Incidence matrix according to Dynkin symbol

```Qqo oxx3xxo3oox4xxx&#zxt

o.. o..3o..3o..4o..     | 192   *   * |   4   2   2   0   0   0   0   0   0  0 |   2   2   4  1   1   4   4   0   0   0  0   0   0   0   0  0  0  0  0 |  1  2  2   2   2   2   4  2  0  0  0   0   0   0   0  0  0 | 1  1  2  1  2  0 0
.o. .o.3.o.3.o.4.o.     |   * 384   * |   0   0   1   1   2   2   2   0   0  0 |   0   0   0  0   1   2   2   2   1   2  1   2   2   1   2  0  0  0  0 |  0  0  0   2   2   1   2  1  1  1  1   1   2   1   2  0  0 | 0  1  2  1  1  1 1
..o ..o3..o3..o4..o     |   *   * 192 |   0   0   0   0   0   0   4   2   2  1 |   0   0   0  0   0   0   0   0   0   0  0   4   2   4   4  1  2  2  1 |  0  0  0   2   0   0   0  0  0  0  2   4   4   2   2  1  1 | 0  2  2  0  0  2 1
------------------------+-------------+----------------------------------------+-----------------------------------------------------------------------+------------------------------------------------------------+-------------------
... ... x.. ... ...     |   2   0   0 | 384   *   *   *   *   *   *   *   *  * |   1   1   1  0   0   1   0   0   0   0  0   0   0   0   0  0  0  0  0 |  1  1  1   1   0   1   1  0  0  0  0   0   0   0   0  0  0 | 1  1  1  0  1  0 0
... ... ... ... x..     |   2   0   0 |   * 192   *   *   *   *   *   *   *  * |   0   0   2  1   0   0   2   0   0   0  0   0   0   0   0  0  0  0  0 |  0  1  2   0   1   0   2  2  0  0  0   0   0   0   0  0  0 | 1  0  1  1  2  0 0
oo. oo.3oo.3oo.4oo.&#x  |   1   1   0 |   *   * 384   *   *   *   *   *   *  * |   0   0   0  0   1   2   2   0   0   0  0   0   0   0   0  0  0  0  0 |  0  0  0   2   2   1   2  1  0  0  0   0   0   0   0  0  0 | 0  1  2  1  1  0 0
... .x. ... ... ...     |   0   2   0 |   *   *   * 192   *   *   *   *   *  * |   0   0   0  0   1   0   0   2   0   0  0   2   0   0   0  0  0  0  0 |  0  0  0   2   2   0   0  0  1  0  0   1   2   0   0  0  0 | 0  1  2  1  0  1 0
... ... .x. ... ...     |   0   2   0 |   *   *   *   * 384   *   *   *   *  * |   0   0   0  0   0   1   0   0   1   1  0   0   1   0   0  0  0  0  0 |  0  0  0   1   0   1   1  0  0  1  0   0   0   1   1  0  0 | 0  1  1  0  1  0 1
... ... ... ... .x.     |   0   2   0 |   *   *   *   *   * 384   *   *   *  * |   0   0   0  0   0   0   1   1   0   1  1   0   0   0   1  0  0  0  0 |  0  0  0   0   1   0   1  1  1  1  1   0   1   0   1  0  0 | 0  0  1  1  1  1 1
.oo .oo3.oo3.oo4.oo&#x  |   0   1   1 |   *   *   *   *   *   * 768   *   *  * |   0   0   0  0   0   0   0   0   0   0  0   1   1   1   1  0  0  0  0 |  0  0  0   1   0   0   0  0  0  0  1   1   1   1   1  0  0 | 0  1  1  0  0  1 1
... ..x ... ... ...     |   0   0   2 |   *   *   *   *   *   *   * 192   *  * |   0   0   0  0   0   0   0   0   0   0  0   2   0   0   0  1  1  1  0 |  0  0  0   2   0   0   0  0  0  0  0   2   2   0   0  1  1 | 0  2  2  0  0  1 0
... ... ... ..x ...     |   0   0   2 |   *   *   *   *   *   *   *   * 192  * |   0   0   0  0   0   0   0   0   0   0  0   0   0   2   0  0  1  0  1 |  0  0  0   0   0   0   0  0  0  0  1   2   0   2   0  1  0 | 0  2  0  0  0  1 1
... ... ... ... ..x     |   0   0   2 |   *   *   *   *   *   *   *   *   * 96 |   0   0   0  0   0   0   0   0   0   0  0   0   0   0   4  0  0  2  0 |  0  0  0   0   0   0   0  0  0  0  2   0   4   0   2  0  1 | 0  0  2  0  0  2 1
------------------------+-------------+----------------------------------------+-----------------------------------------------------------------------+------------------------------------------------------------+-------------------
... o..3x.. ... ...     |   3   0   0 |   3   0   0   0   0   0   0   0   0  0 | 128   *   *  *   *   *   *   *   *   *  *   *   *   *   *  *  *  *  * |  1  1  0   1   0   0   0  0  0  0  0   0   0   0   0  0  0 | 1  1  1  0  0  0 0
... ... x..3o.. ...     |   3   0   0 |   3   0   0   0   0   0   0   0   0  0 |   * 128   *  *   *   *   *   *   *   *  *   *   *   *   *  *  *  *  * |  1  0  1   0   0   1   0  0  0  0  0   0   0   0   0  0  0 | 1  1  0  0  1  0 0
... ... x.. ... x..     |   4   0   0 |   2   2   0   0   0   0   0   0   0  0 |   *   * 192  *   *   *   *   *   *   *  *   *   *   *   *  *  *  *  * |  0  1  1   0   0   0   1  0  0  0  0   0   0   0   0  0  0 | 1  0  1  0  1  0 0
... ... ... o..4x..     |   4   0   0 |   0   4   0   0   0   0   0   0   0  0 |   *   *   * 48   *   *   *   *   *   *  *   *   *   *   *  *  *  *  * |  0  0  2   0   0   0   0  2  0  0  0   0   0   0   0  0  0 | 1  0  0  1  2  0 0
... ox. ... ... ...&#x  |   1   2   0 |   0   0   2   1   0   0   0   0   0  0 |   *   *   *  * 192   *   *   *   *   *  *   *   *   *   *  *  *  *  * |  0  0  0   2   2   0   0  0  0  0  0   0   0   0   0  0  0 | 0  1  2  1  0  0 0
... ... xx. ... ...&#x  |   2   2   0 |   1   0   2   0   1   0   0   0   0  0 |   *   *   *  *   * 384   *   *   *   *  *   *   *   *   *  *  *  *  * |  0  0  0   1   0   1   1  0  0  0  0   0   0   0   0  0  0 | 0  1  1  0  1  0 0
... ... ... ... xx.&#x  |   2   2   0 |   0   1   2   0   0   1   0   0   0  0 |   *   *   *  *   *   * 384   *   *   *  *   *   *   *   *  *  *  *  * |  0  0  0   0   1   0   1  1  0  0  0   0   0   0   0  0  0 | 0  0  1  1  1  0 0
... .x. ... ... .x.     |   0   4   0 |   0   0   0   2   0   2   0   0   0  0 |   *   *   *  *   *   *   * 192   *   *  *   *   *   *   *  *  *  *  * |  0  0  0   0   1   0   0  0  1  0  0   0   1   0   0  0  0 | 0  0  1  1  0  1 0
... ... .x.3.o. ...     |   0   3   0 |   0   0   0   0   3   0   0   0   0  0 |   *   *   *  *   *   *   *   * 128   *  *   *   *   *   *  *  *  *  * |  0  0  0   0   0   1   0  0  0  1  0   0   0   1   0  0  0 | 0  1  0  0  1  0 1
... ... .x. ... .x.     |   0   4   0 |   0   0   0   0   2   2   0   0   0  0 |   *   *   *  *   *   *   *   *   * 192  *   *   *   *   *  *  *  *  * |  0  0  0   0   0   0   1  0  0  1  0   0   0   0   1  0  0 | 0  0  1  0  1  0 1
... ... ... .o.4.x.     |   0   4   0 |   0   0   0   0   0   4   0   0   0  0 |   *   *   *  *   *   *   *   *   *   * 96   *   *   *   *  *  *  *  * |  0  0  0   0   0   0   0  1  1  1  1   0   0   0   0  0  0 | 0  0  0  1  1  1 1
... .xx ... ... ...&#x  |   0   2   2 |   0   0   0   1   0   0   2   1   0  0 |   *   *   *  *   *   *   *   *   *   *  * 384   *   *   *  *  *  *  * |  0  0  0   1   0   0   0  0  0  0  0   1   1   0   0  0  0 | 0  1  1  0  0  1 0
... ... .xo ... ...&#x  |   0   2   1 |   0   0   0   0   1   0   2   0   0  0 |   *   *   *  *   *   *   *   *   *   *  *   * 384   *   *  *  *  *  * |  0  0  0   1   0   0   0  0  0  0  0   0   0   1   1  0  0 | 0  1  1  0  0  0 1
... ... ... .ox ...&#x  |   0   1   2 |   0   0   0   0   0   0   2   0   1  0 |   *   *   *  *   *   *   *   *   *   *  *   *   * 384   *  *  *  *  * |  0  0  0   0   0   0   0  0  0  0  1   1   0   1   0  0  0 | 0  1  0  0  0  1 1
... ... ... ... .xx&#x  |   0   2   2 |   0   0   0   0   0   1   2   0   0  1 |   *   *   *  *   *   *   *   *   *   *  *   *   *   * 384  *  *  *  * |  0  0  0   0   0   0   0  0  0  0  1   0   1   0   1  0  0 | 0  0  1  0  0  1 1
... ..x3..o ... ...     |   0   0   3 |   0   0   0   0   0   0   0   3   0  0 |   *   *   *  *   *   *   *   *   *   *  *   *   *   *   * 64  *  *  * |  0  0  0   2   0   0   0  0  0  0  0   0   0   0   0  1  1 | 0  2  2  0  0  0 0
... ..x ... ..x ...     |   0   0   4 |   0   0   0   0   0   0   0   2   2  0 |   *   *   *  *   *   *   *   *   *   *  *   *   *   *   *  * 96  *  * |  0  0  0   0   0   0   0  0  0  0  0   2   0   0   0  1  0 | 0  2  0  0  0  1 0
... ..x ... ... ..x     |   0   0   4 |   0   0   0   0   0   0   0   2   0  2 |   *   *   *  *   *   *   *   *   *   *  *   *   *   *   *  *  * 96  * |  0  0  0   0   0   0   0  0  0  0  0   0   2   0   0  0  1 | 0  0  2  0  0  1 0
... ... ..o3..x ...     |   0   0   3 |   0   0   0   0   0   0   0   0   3  0 |   *   *   *  *   *   *   *   *   *   *  *   *   *   *   *  *  *  * 64 |  0  0  0   0   0   0   0  0  0  0  0   0   0   2   0  1  0 | 0  2  0  0  0  0 1
------------------------+-------------+----------------------------------------+-----------------------------------------------------------------------+------------------------------------------------------------+-------------------
... o..3x..3o.. ...     ♦   6   0   0 |  12   0   0   0   0   0   0   0   0  0 |   4   4   0  0   0   0   0   0   0   0  0   0   0   0   0  0  0  0  0 | 32  *  *   *   *   *   *  *  *  *  *   *   *   *   *  *  * | 1  1  0  0  0  0 0
... o..3x.. ... x..     ♦   6   0   0 |   6   3   0   0   0   0   0   0   0  0 |   2   0   3  0   0   0   0   0   0   0  0   0   0   0   0  0  0  0  0 |  * 64  *   *   *   *   *  *  *  *  *   *   *   *   *  *  * | 1  0  1  0  0  0 0
... ... x..3o..4x..     ♦  24   0   0 |  24  24   0   0   0   0   0   0   0  0 |   0   8  12  6   0   0   0   0   0   0  0   0   0   0   0  0  0  0  0 |  *  * 16   *   *   *   *  *  *  *  *   *   *   *   *  *  * | 1  0  0  0  1  0 0
... oxx3xxo ... ...&#xt ♦   3   6   3 |   3   0   6   3   3   0   6   3   0  0 |   1   0   0  0   3   3   0   0   0   0  0   3   3   0   0  1  0  0  0 |  *  *  * 128   *   *   *  *  *  *  *   *   *   *   *  *  * | 0  1  1  0  0  0 0
... ox. ... ... xx.&#x  ♦   2   4   0 |   0   1   4   2   0   2   0   0   0  0 |   0   0   0  0   2   0   2   1   0   0  0   0   0   0   0  0  0  0  0 |  *  *  *   * 192   *   *  *  *  *  *   *   *   *   *  *  * | 0  0  1  1  0  0 0
... ... xx.3oo. ...&#x  ♦   3   3   0 |   3   0   3   0   3   0   0   0   0  0 |   0   1   0  0   0   3   0   0   1   0  0   0   0   0   0  0  0  0  0 |  *  *  *   *   * 128   *  *  *  *  *   *   *   *   *  *  * | 0  1  0  0  1  0 0
... ... xx. ... xx.&#x  ♦   4   4   0 |   2   2   4   0   2   2   0   0   0  0 |   0   0   1  0   0   2   2   0   0   1  0   0   0   0   0  0  0  0  0 |  *  *  *   *   *   * 192  *  *  *  *   *   *   *   *  *  * | 0  0  1  0  1  0 0
... ... ... oo.4xx.&#x  ♦   4   4   0 |   0   4   4   0   0   4   0   0   0  0 |   0   0   0  1   0   0   4   0   0   0  1   0   0   0   0  0  0  0  0 |  *  *  *   *   *   *   * 96  *  *  *   *   *   *   *  *  * | 0  0  0  1  1  0 0
... .x. ... .o.4.x.     ♦   0   8   0 |   0   0   0   4   0   8   0   0   0  0 |   0   0   0  0   0   0   0   4   0   0  2   0   0   0   0  0  0  0  0 |  *  *  *   *   *   *   *  * 48  *  *   *   *   *   *  *  * | 0  0  0  1  0  1 0
... ... .x.3.o.4.x.     ♦   0  24   0 |   0   0   0   0  24  24   0   0   0  0 |   0   0   0  0   0   0   0   0   8  12  6   0   0   0   0  0  0  0  0 |  *  *  *   *   *   *   *  *  * 16  *   *   *   *   *  *  * | 0  0  0  0  1  0 1
.qo ... ... .ox4.xx&#zx ♦   0   8   8 |   0   0   0   0   0   8  16   0   4  4 |   0   0   0  0   0   0   0   0   0   0  2   0   0   8   8  0  0  0  0 |  *  *  *   *   *   *   *  *  *  * 48   *   *   *   *  *  * | 0  0  0  0  0  1 1
... .xx ... .ox ...&#x  ♦   0   2   4 |   0   0   0   1   0   0   4   2   2  0 |   0   0   0  0   0   0   0   0   0   0  0   2   0   2   0  0  1  0  0 |  *  *  *   *   *   *   *  *  *  *  * 192   *   *   *  *  * | 0  1  0  0  0  1 0
... .xx ... ... .xx&#x  ♦   0   4   4 |   0   0   0   2   0   2   4   2   0  2 |   0   0   0  0   0   0   0   1   0   0  0   2   0   0   2  0  0  1  0 |  *  *  *   *   *   *   *  *  *  *  *   * 192   *   *  *  * | 0  0  1  0  0  1 0
... ... .xo3.ox ...&#x  ♦   0   3   3 |   0   0   0   0   3   0   6   0   3  0 |   0   0   0  0   0   0   0   0   1   0  0   0   3   3   0  0  0  0  1 |  *  *  *   *   *   *   *  *  *  *  *   *   * 128   *  *  * | 0  1  0  0  0  0 1
... ... .xo ... .xx&#x  ♦   0   4   2 |   0   0   0   0   2   2   4   0   0  1 |   0   0   0  0   0   0   0   0   0   1  0   0   2   0   2  0  0  0  0 |  *  *  *   *   *   *   *  *  *  *  *   *   *   * 192  *  * | 0  0  1  0  0  0 1
... ..x3..o3..x ...     ♦   0   0  12 |   0   0   0   0   0   0   0  12  12  0 |   0   0   0  0   0   0   0   0   0   0  0   0   0   0   0  4  6  0  4 |  *  *  *   *   *   *   *  *  *  *  *   *   *   *   * 16  * | 0  2  0  0  0  0 0
... ..x3..o ... ..x     ♦   0   0   6 |   0   0   0   0   0   0   0   6   0  3 |   0   0   0  0   0   0   0   0   0   0  0   0   0   0   0  2  0  3  0 |  *  *  *   *   *   *   *  *  *  *  *   *   *   *   *  * 32 | 0  0  2  0  0  0 0
------------------------+-------------+----------------------------------------+-----------------------------------------------------------------------+------------------------------------------------------------+-------------------
... o..3x..3o..4x..     ♦  96   0   0 | 192  96   0   0   0   0   0   0   0  0 |  64  64  96 24   0   0   0   0   0   0  0   0   0   0   0  0  0  0  0 | 16 32  8   0   0   0   0  0  0  0  0   0   0   0   0  0  0 | 2  *  *  *  *  * *
... oxx3xxo3oox ...&#xt ♦   6  12  12 |  12   0  12   6  12   0  24  12  12  0 |   4   4   0  0   6  12   0   0   4   0  0  12  12  12   0  4  6  0  4 |  1  0  0   4   0   4   0  0  0  0  0   6   0   4   0  1  0 | * 32  *  *  *  * *
... oxx3xxo ... xxx&#xt ♦   6  12   6 |   6   3  12   6   6   6  12   6   0  3 |   2   0   3  0   6   6   6   3   0   3  0   6   6   0   6  2  0  3  0 |  0  1  0   2   3   0   3  0  0  0  0   0   3   0   3  0  1 | *  * 64  *  *  * *
... ox. ... oo.4xx.&#x  ♦   4   8   0 |   0   4   8   4   0   8   0   0   0  0 |   0   0   0  1   4   0   8   4   0   0  2   0   0   0   0  0  0  0  0 |  0  0  0   0   4   0   0  2  1  0  0   0   0   0   0  0  0 | *  *  * 48  *  * *
... ... xx.3oo.4xx.&#x  ♦  24  24   0 |  24  24  24   0  24  24   0   0   0  0 |   0   8  12  6   0  24  24   0   8  12  6   0   0   0   0  0  0  0  0 |  0  0  1   0   0   8  12  6  0  1  0   0   0   0   0  0  0 | *  *  *  * 16  * *
.qo .xx ... .ox4.xx&#zx ♦   0  16  16 |   0   0   0   8   0  16  32   8   8  8 |   0   0   0  0   0   0   0   8   0   0  4  16   0  16  16  0  4  4  0 |  0  0  0   0   0   0   0  0  2  0  2   8   8   0   0  0  0 | *  *  *  *  * 24 *
.qo ... .xo3.ox4.xx&#zx ♦   0  48  24 |   0   0   0   0  48  48  96   0  24 12 |   0   0   0  0   0   0   0   0  16  24 12   0  48  48  48  0  0  0  8 |  0  0  0   0   0   0   0  0  0  2  6   0   0  16  24  0  0 | *  *  *  *  *  * 8
```